Fabrication and Fractality of Fe 2 O 3-CeO 2 / ZSM-5 Composites for High-Temperature Desulfurization

Fe2O3/ZSM-5 modified with Ce via citrate route (sol-gel approach) is applied for H2S removal in 500–700 ◦C temperature range. The sulfidation activity of Fe2O3/ZSM-5 is appreciably promoted by introduction of Ce plausibly attributed to the synergy of Fe2O3 and CeO2. 5Fe5Ce/ZSM-5 performs the optimal desulfurization behavior at 600 ◦C with sulfur capacity of 1020 μmol S/g, and the sulfidation process conforms to non-catalytic gas-solid redox reaction mechanism, which yields FeS2, Ce2S3, and S. Fractal analysis is introduced to evaluate the surface porous structure and the adsorption capacity of the sorbent. Its surface fractal dimension is estimated by using Frenkel-Halsey-Hill (FHH) model. It considerably increases after sulfidation plausibly attributed to the formation of a few heterogeneous sulfides or elemental sulfur, which block or cover the surface pore structures of sorbents.


Introduction
Gasification and gasification-integrated energy conversion system, such as Integrated Coal Gasification Combined Cycle (IGCC) power generation system, has been considered as one of the most potential clean coal technologies in 21st century.It can greatly enhance the power generation efficiency and lower the pollutant emissions causing environmental pollution [1][2][3].In an IGCC power plant, hot coal gas containing amounts of sulfur compounds is first purified and then introduced into gas turbines for generating electricity.H 2 S is the major sulfur compound in the hot coal gas and it needs to be eliminated before utilization for the sake of protecting the turbine leaves from corrosion and guarantying the lower sulfur emission [4,5].Therefore, high-temperature desulfurizer plays a crucial role in IGCC technology.
Many metal oxides have been applied for high-temperature desulfurization, such as, ZnO [6,7], CuO [8,9], MnO x [10,11], and CeO 2 [12][13][14].However, iron oxide is the most widely used sorbent for hot coal gas desulfurization in the field of the coal chemical industry owing to its good adsorption capacity, abundant resource, lower cost, and good physical strength [15][16][17][18][19]. Doping cerium ion (Ce 4+ ) into Fe 2 O 3 lattice can generate more oxygen vacancies which facilitate the activation and transport of the oxygen species.The generated surface oxygen vacancies and bulk oxygen species with relatively high mobility are favorable for sulfur removal [20].However, unsupported sorbents often suffer from sintering and low mechanical strength, thus, Fe 2 O 3 -CeO 2 mixed oxides are deposited onto ZSM-5 with a good surface area and pore structures to alleviate these problems.
The Fe 2 O 3 -CeO 2 /ZSM-5 sorbents with various Fe/Ce molar ratios are fabricated via citrate route and characterized by nitrogen adsorption-desorption isotherms, scanning electron microscope (SEM), X-ray diffraction (XRD) techniques, and hydrogen temperature programmed reduction (H 2 -TPR).The H 2 S adsorption tests are performed to study the effects of reaction temperature and CeO 2 content (SEM), X-ray diffraction (XRD) techniques, and hydrogen temperature programmed reduction (H2-TPR).The H2S adsorption tests are performed to study the effects of reaction temperature and CeO2 content on the desulfurization performance of Fe2O3-based sorbents, and the process of H2S adsorption on Fe2O3-CeO2/ZSM-5 are then discussed.To obtain a better understanding of the textural structure or surface characteristics of the sorbent, fractal analysis is employed to address the changes in sorbent fractality or surface fractal dimension before and after sulfidation reaction, which aims to enrich the knowledge about the fractal nature of Fe2O3-based sorbents.

Characterization Analysis
The SEM images of ZSM-5, fresh and spent 5Fe5Ce/ZSM-5 are presented in Figure 1.ZSM-5 comprises of a few rectangular granules with smooth and angular surface (Figure 1a,b).The rectangular ZSM-5 particles can be observed in fresh and spent sorbents as well, and the teeny particles on ZSM-5 surface in fresh 5Fe5Ce/ZSM-5 are likely assigned to the active phases of cerium oxides and iron oxides (Figure 1c).After sulfidation, amounts of porous aggregates related to sulfides or elemental sulfur are detected in the spent 5Fe5Ce/ZSM-5 (Figure 1d).The sorbent textural features are examined using nitrogen adsorption-desorption techniques, ZSM-5, fresh and spent 5Fe5Ce/ZSM-5 all show typical feature of Type I nitrogen adsorption isotherm (Figure 2a), indicating that micropore structures present in the ZSM-5 and the sorbents.However, the nitrogen uptake decreases after calcination and desulfurization processes, probably because that the active metal oxides and the sulfidation products may block or cover the pore structures on ZSM-5 surface, which can be further verified from the decrease in volume values of ~3.89 nm pore structures (Figure 2b).The surface area and total pore volume of ZSM-5 are 320 m 2 /g and 255 mm 3 /g respectively, the surface area decreases to 170 and 116 m 2 /g, the total pore volume reduces to 119 and 78 mm 3 /g after calcination and sulfidation processes relatively (Table 1).However, the average pore diameter slightly diminishes from 3.19 nm to 2.79 and 2.69 nm correspondingly.The sorbent textural features are examined using nitrogen adsorption-desorption techniques, ZSM-5, fresh and spent 5Fe5Ce/ZSM-5 all show typical feature of Type I nitrogen adsorption isotherm (Figure 2a), indicating that micropore structures present in the ZSM-5 and the sorbents.However, the nitrogen uptake decreases after calcination and desulfurization processes, probably because that the active metal oxides and the sulfidation products may block or cover the pore structures on ZSM-5 surface, which can be further verified from the decrease in volume values of ~3.89 nm pore structures (Figure 2b).The surface area and total pore volume of ZSM-5 are 320 m 2 /g and 255 mm 3 /g respectively, the surface area decreases to 170 and 116 m 2 /g, the total pore volume reduces to 119 and 78 mm 3 /g after calcination and sulfidation processes relatively (Table 1).However, the average pore diameter slightly diminishes from 3.19 nm to 2.79 and 2.69 nm correspondingly.Table 1.Brunauer-Emmett-Teller (BET) specific surface area (SBET), total pore volume (Vtotal), micropore volume (Vmicro), mesopore volume (Vmeso), average pore diameter (Daver) of ZSM-5, fresh and spent 5Fe5Ce/ZSM-5.The XRD profiles of ZSM-5, fresh and spent sorbents are shown in Figure 3, ZSM-5 presents a conspicuous diffraction peak at 2θ = ~23°, it can be clearly observed in fresh and spent sorbents, and its intensity only slightly reduce after preparation and sulfidation processes (Figure 3a), suggesting that it has a good thermal stability.3b).Thus, sulfidation of 5Fe5Ce/ZSM-5 yields FeS2, Ce2S3, and S. The crystalline sizes of the pristine ZSM-5 and the ZSM-5 loaded with metal oxides are estimated from the calculation of its (3 3 0) lattice plane, the crystalline size of the pristine ZSM-5 is 56 nm, which slightly decreases after loading metal oxides and sulfidation reaction.With rising CeO2 doping ratios, the Fe2O3 peaks of fresh xFeyCe/ZSM-5 generally shift towards higher diffraction angles, plausibly suggesting the expansion of Fe2O3 lattice, the crystalline sizes of Fe2O3 estimated from the calculation of its (1 1 0) lattice plane range from 18 to 65 nm, while the CeO2 peaks of fresh xFeyCe/ZSM-5 generally shift toward lower diffraction angles, probably indicating the contraction of CeO2 lattice.The crystalline size of CeO2 in fresh 5Fe5Ce/ZSM-5 estimated from the calculation of its (1 1 1) lattice plane is 21.12 nm, it appreciably increases to 24.99 nm due to the formation of Ce2S3 product after sulfidation, which suggests that the CeO2 crystalline grains in fresh 5Fe5Ce/ZSM-5 probably aggregate during high-temperature desulfurization.

SBET
The H2-TPR profiles of xFeyCe/ZSM-5 sorbents are shown in Figure 4, the adsorption peaks at 352-387 °C are related to the reduction of Fe2O3 to Fe4O3, then Fe4O3 will be reduced to FeO at high temperature of 534-605 °C [21].The major reduction peaks slightly shift towards lower temperature with increasing CeO2 adding amount from 10 at.% to 50 at.%, which indicates that doping CeO2 into Fe2O3 lattice can improve the sorbent reducibility.However, the reduction peaks obviously shift to a higher temperature when CeO2 molar fraction exceeds 50 at.%, which suggests that excessive CeO2 would inhibit the reduction of the sorbent.Table 1.Brunauer-Emmett-Teller (BET) specific surface area (S BET ), total pore volume (V total ), micropore volume (V micro ), mesopore volume (V meso ), average pore diameter (D aver ) of ZSM-5, fresh and spent 5Fe5Ce/ZSM-5.The XRD profiles of ZSM-5, fresh and spent sorbents are shown in Figure 3, ZSM-5 presents a conspicuous diffraction peak at 2θ = ~23 • , it can be clearly observed in fresh and spent sorbents, and its intensity only slightly reduce after preparation and sulfidation processes (Figure 3a), suggesting that it has a good thermal stability.3b).Thus, sulfidation of 5Fe5Ce/ZSM-5 yields FeS 2 , Ce 2 S 3 , and S. The crystalline sizes of the pristine ZSM-5 and the ZSM-5 loaded with metal oxides are estimated from the calculation of its (3 3 0) lattice plane, the crystalline size of the pristine ZSM-5 is 56 nm, which slightly decreases after loading metal oxides and sulfidation reaction.With rising CeO 2 doping ratios, the Fe 2 O 3 peaks of fresh xFeyCe/ZSM-5 generally shift towards higher diffraction angles, plausibly suggesting the expansion of Fe 2 O 3 lattice, the crystalline sizes of Fe 2 O 3 estimated from the calculation of its (1 1 0) lattice plane range from 18 to 65 nm, while the CeO 2 peaks of fresh xFeyCe/ZSM-5 generally shift toward lower diffraction angles, probably indicating the contraction of CeO 2 lattice.The crystalline size of CeO 2 in fresh 5Fe5Ce/ZSM-5 estimated from the calculation of its (1 1 1) lattice plane is 21.12 nm, it appreciably increases to 24.99 nm due to the formation of Ce 2 S 3 product after sulfidation, which suggests that the CeO 2 crystalline grains in fresh 5Fe5Ce/ZSM-5 probably aggregate during high-temperature desulfurization.

Sample
The H 2 -TPR profiles of xFeyCe/ZSM-5 sorbents are shown in Figure 4, the adsorption peaks at 352-387 • C are related to the reduction of Fe 2 O 3 to Fe 4 O 3 , then Fe 4 O 3 will be reduced to FeO at high temperature of 534-605 • C [21].The major reduction peaks slightly shift towards lower temperature with increasing CeO 2 adding amount from 10 at.% to 50 at.%, which indicates that doping CeO 2 into Fe 2 O 3 lattice can improve the sorbent reducibility.However, the reduction peaks obviously shift to a higher temperature when CeO 2 molar fraction exceeds 50 at.%, which suggests that excessive CeO 2 would inhibit the reduction of the sorbent.

Effect of Reaction Temperature
The breakthrough time of 5Fe5Ce/ZSM-5 first increases and then decreases with the elevation of reaction temperature (Figure 5a).5Fe5Ce/ZSM-5 offers a good H2S removal ability at 600 °C.5Fe5Ce/ZSM-5 performs the greatest sulfur capacity of 1020 µmol S/g and the longest breakthrough time of 20 min.The H2S reaction rate with metal oxides and the H2S diffusion rate can be promoted by increasing the reaction temperatures, the breakthrough time of 5 min and sulfur capacity of 408 µmol S/g over 5Fe5Ce/ZSM-5 at 500 °C are very low by the reason of lower H2S diffusion rate, and only the metal oxides on the sorbent surface react (Figure 5b).When the reaction temperature increases from 600 to 700 °C, the breakthrough time and sulfur capacity drop from 20 min and 1020 µmol S/g to 10 min and 408 µmol S/g correspondingly, and the breakthrough curve becomes flatter with lower slope, possibly due to the limitation of H2S diffusion for the reason that some active phases sinter or aggregate at 700 °C.Thus, the optimum temperature of sulfidation process is 600 °C [22,23].

Effect of CeO2 Content
The H2S breakthrough curves and sulfur capacities of ZSM-5 and different sorbents are depicted in Figure 6, ZSM-5 is almost immediately broken through with sulfur capacity of nearly zero, suggesting that ZSM-5 is inert to hydrogen sulfide.The pure CeO2 and Fe2O3 present fairly poor desulfurization performances with short breakthrough time of ~5 min and lower sulfur capacity of ~400 µmol S/g.The breakthrough time of Fe2O3-based sorbents is only 5-10 min by addition of 10-30 at.% CeO2, it suddenly increases to 20 min with CeO2 molar fraction rising to 50 at.%.However, the breakthrough time and sulfur capacity slightly decrease to 15 min and 816 µmol S/g respectively with

Effect of Reaction Temperature
The breakthrough time of 5Fe5Ce/ZSM-5 first increases and then decreases with the elevation of reaction temperature (Figure 5a).5Fe5Ce/ZSM-5 offers a good H2S removal ability at 600 °C.5Fe5Ce/ZSM-5 performs the greatest sulfur capacity of 1020 µmol S/g and the longest breakthrough time of 20 min.The H2S reaction rate with metal oxides and the H2S diffusion rate can be promoted by increasing the reaction temperatures, the breakthrough time of 5 min and sulfur capacity of 408 µmol S/g over 5Fe5Ce/ZSM-5 at 500 °C are very low by the reason of lower H2S diffusion rate, and only the metal oxides on the sorbent surface react (Figure 5b).When the reaction temperature increases from 600 to 700 °C, the breakthrough time and sulfur capacity drop from 20 min and 1020 µmol S/g to 10 min and 408 µmol S/g correspondingly, and the breakthrough curve becomes flatter with lower slope, possibly due to the limitation of H2S diffusion for the reason that some active phases sinter or aggregate at 700 °C.Thus, the optimum temperature of sulfidation process is 600 °C [22,23].

Effect of CeO2 Content
The H2S breakthrough curves and sulfur capacities of ZSM-5 and different sorbents are depicted in Figure 6, ZSM-5 is almost immediately broken through with sulfur capacity of nearly zero, suggesting that ZSM-5 is inert to hydrogen sulfide.The pure CeO2 and Fe2O3 present fairly poor desulfurization performances with short breakthrough time of ~5 min and lower sulfur capacity of ~400 µmol S/g.The breakthrough time of Fe2O3-based sorbents is only 5-10 min by addition of 10-30 at.% CeO2, it suddenly increases to 20 min with CeO2 molar fraction rising to 50 at.%.However, the

Effect of Reaction Temperature
The breakthrough time of 5Fe5Ce/ZSM-5 first increases and then decreases with the elevation of reaction temperature (Figure 5a).5Fe5Ce/ZSM-5 offers a good H 2 S removal ability at 600 • C. 5Fe5Ce/ZSM-5 performs the greatest sulfur capacity of 1020 µmol S/g and the longest breakthrough time of 20 min.The H 2 S reaction rate with metal oxides and the H 2 S diffusion rate can be promoted by increasing the reaction temperatures, the breakthrough time of 5 min and sulfur capacity of 408 µmol S/g over 5Fe5Ce/ZSM-5 at 500 • C are very low by the reason of lower H 2 S diffusion rate, and only the metal oxides on the sorbent surface react (Figure 5b).When the reaction temperature increases from 600 to 700 • C, the breakthrough time and sulfur capacity drop from 20 min and 1020 µmol S/g to 10 min and 408 µmol S/g correspondingly, and the breakthrough curve becomes flatter with lower slope, possibly due to the limitation of H 2 S diffusion for the reason that some active phases sinter or aggregate at 700 • C. Thus, the optimum temperature of sulfidation process is 600 • C [22,23].

Effect of CeO 2 Content
The H 2 S breakthrough curves and sulfur capacities of ZSM-5 and different sorbents are depicted in Figure 6, ZSM-5 is almost immediately broken through with sulfur capacity of nearly zero, suggesting that ZSM-5 is inert to hydrogen sulfide.The pure CeO

Reusability
The H2S breakthrough curves and sulfur capacities of three successive desulfurization and regeneration (regenerated by 5% O2/N2 mixture) cycles over 5Fe5Ce/ZSM-5 at identical temperature of 600 °C and gas flow rate of 30,000 mL•h −1 •g −1 are presented in Figure 7.The desulfurization performance reduces a little bit after the first cycle, and the sulfur capacity decreases from 1020 µmol S/g to 811 µmol S/g, plausibly because the active phases (Fe2O3 and CeO2) aggregate or sinter during the high-temperature sulfidation and regeneration processes.However, the sulfur capacity nearly does not change after the second cycle and stays at ~800 µmol S/g.

Reusability
The H 2 S breakthrough curves and sulfur capacities of three successive desulfurization and regeneration (regenerated by 5% O 2 /N 2 mixture) cycles over 5Fe5Ce/ZSM-5 at identical temperature of 600 • C and gas flow rate of 30,000 mL•h −1 •g −1 are presented in Figure 7.The desulfurization performance reduces a little bit after the first cycle, and the sulfur capacity decreases from 1020 µmol S/g to 811 µmol S/g, plausibly because the active phases (Fe 2 O 3 and CeO 2 ) aggregate or sinter during the high-temperature sulfidation and regeneration processes.However, the sulfur capacity nearly does not change after the second cycle and stays at ~800 µmol S/g.

Sorbent Characterization
The surface micro-morphologies of ZSM-5, fresh and spent sorbents are measured using field emission scanning electron microscopy (Phillips XL-30 FEG/NEW, Eindhoven, The Netherlands), their textural properties are determined via nitrogen adsorption-desorption isotherm (Micromeritics ASAP 2020, Norcross, GA, USA), and their pore size distributions are obtained from Barrett-Joyner-Halenda (BJH) formula using the desorption branch of nitrogen isotherm.XRD patterns are attained on an X-ray diffractometer (Bruker D8 Advance, Karlsruhe, Germany), the crystalline sizes are estimated from Debye-Scherrer formula, and redox properties are examined via H2-TPR (ChemiSorb 2720 chemisorption analyzer from Micromeritics Instrument Corp., Norcross, GA, USA), the specimens are heated from room temperature to 700 °C in a 10% H2/Ar mixture with a flow rate of 40 mL/min at a rate of 10 °C/min.

Adsorption
H2S adsorption tests are carried out in a vertical fixed-bed microreactor loaded with 0.2 g sorbents [27,28], the H2S breakthrough concentration is determined as 50 mg/m 3 .The flow rate (30,000 mL•h −1 •g −1 ) of feeding gas (0.2% H2S/N2 mixture) are precisely controlled by mass flow controllers.The sorbents are firstly heated up to the desired reaction temperature in N2 to remove the impurities adsorbed on the sorbent surface prior to hydrogen sulfide adsorption.After sulfidation tests, pure N2

Sorbent Characterization
The surface micro-morphologies of ZSM-5, fresh and spent sorbents are measured using field emission scanning electron microscopy (Phillips XL-30 FEG/NEW, Eindhoven, The Netherlands), their textural properties are determined via nitrogen adsorption-desorption isotherm (Micromeritics ASAP 2020, Norcross, GA, USA), and their pore size distributions are obtained from Barrett-Joyner-Halenda (BJH) formula using the desorption branch of nitrogen isotherm.XRD patterns are attained on an X-ray diffractometer (Bruker D8 Advance, Karlsruhe, Germany), the crystalline sizes are estimated from Debye-Scherrer formula, and redox properties are examined via H 2 -TPR (ChemiSorb 2720 chemisorption analyzer from Micromeritics Instrument Corp., Norcross, GA, USA), the specimens are heated from room temperature to 700 • C in a 10% H 2 /Ar mixture with a flow rate of 40 mL/min at a rate of 10 • C/min.

Adsorption
H 2 S adsorption tests are carried out in a vertical fixed-bed microreactor loaded with 0.2 g sorbents [27,28], the H 2 S breakthrough concentration is determined as 50 mg/m 3 .The flow rate (30,000 mL•h −1 •g −1 ) of feeding gas (0.2% H 2 S/N 2 mixture) are precisely controlled by mass flow controllers.The sorbents are firstly heated up to the desired reaction temperature in N 2 to remove the impurities adsorbed on the sorbent surface prior to hydrogen sulfide adsorption.After sulfidation tests, pure N 2 purges the desulfurization system until the sorbent bed cools down to ambient temperature.The H 2 S concentration of the outlet gas is measured by a gas chromatograph (Fuli Analytical Instrument Co., Ltd., GC9790IIH-2, Taizhou, China).The breakthrough time is defined as the duration before the breakthrough point, and the breakthrough sulfur capacity is calculated by following formula here S cap denotes the breakthrough sulfur capacity (µmol S/g), W m is the weight hourly space velocity (L•h −1 •g −1 ), V m means molar volume of H 2 S at 1 atm and 25 • C (24.5 L/mol), t stands for the breakthrough time (h), C in and C out denote the inlet and outlet H 2 S concentration (ppm v ), respectively.

Desulfurization Process
According to the XRD analysis, it can be concluded that the sulfidation of 5Fe5Ce/ZSM-5 yields metal sulfides (Ce 2 S 3 and FeS 2 ) and elemental sulfur (S).It follows typical non-catalytic gas-solid redox reaction.The sulfidation reaction can be described with the shrinking core model [29,30].The sulfidation process mainly occurs at the sorbent surface, and the sorbent particles consist of unreacted core and reacted outside product layers.The unreacted core gradually shrinks, but the product layer gradually grows until the whole sorbent particle consumes.The schematic diagram of the sulfidation process is shown in Figure 8, which incorporates five consecutive processes: (1) gaseous H 2 S(g) diffusing from gas bulk onto the sorbent surface forms adsorbed state H 2 S(ad), ( 2) the H 2 S(ad) penetrates through the newly formed product layer to the surface of the unreacted core, (3) the H 2 S(ad) reacts with the active metal oxides of the sorbent, (4) sulfidation products (metal sulfides and elemental sulfur) form new product layer and the reaction product H 2 O(g) penetrates through the product layer to the external surface of the sorbent, and ( 5) the H 2 O(g) continues to diffuse from sorbent external surface to the gas bulk [31,32].
Colloids Interfaces 2017, 1, 10 7 of 11 purges the desulfurization system until the sorbent bed cools down to ambient temperature.The H2S concentration of the outlet gas is measured by a gas chromatograph (Fuli Analytical Instrument Co., Ltd., GC9790IIH-2, Taizhou, China).The breakthrough time is defined as the duration before the breakthrough point, and the breakthrough sulfur capacity is calculated by following formula ( ) here Scap denotes the breakthrough sulfur capacity (µmol S/g), Wm is the weight hourly space velocity (L•h −1 •g −1 ), Vm means molar volume of H2S at 1 atm and 25 °C (24.5 L/mol), t stands for the breakthrough time (h), Cin and Cout denote the inlet and outlet H2S concentration (ppmv), respectively.

Desulfurization Process
According to the XRD analysis, it can be concluded that the sulfidation of 5Fe5Ce/ZSM-5 yields metal sulfides (Ce2S3 and FeS2) and elemental sulfur (S).It follows typical non-catalytic gas-solid redox reaction.The sulfidation reaction can be described with the shrinking core model [29,30].The sulfidation process mainly occurs at the sorbent surface, and the sorbent particles consist of unreacted core and reacted outside product layers.The unreacted core gradually shrinks, but the product layer gradually grows until the whole sorbent particle consumes.The schematic diagram of the sulfidation process is shown in Figure 8, which incorporates five consecutive processes: (1) gaseous H2S(g) diffusing from gas bulk onto the sorbent surface forms adsorbed state H2S(ad), (2) the H2S(ad) penetrates through the newly formed product layer to the surface of the unreacted core, (3) the H2S(ad) reacts with the active metal oxides of the sorbent, (4) sulfidation products (metal sulfides and elemental sulfur) form new product layer and the reaction product H2O(g) penetrates through the product layer to the external surface of the sorbent, and (5) the H2O(g) continues to diffuse from sorbent external surface to the gas bulk [31,32].

Fractal Analysis
In recent decades, fractal analysis has been widely applied in a few fields of scientific researches to characterize the geometric and structural properties of fractal surfaces and pore structures [33,34].Fractal dimension is often adopted to quantitatively evaluate the irregularities of the fractal surface and pore structures.Its value varies from 2 to 3, in which the lowest value 2 corresponds to a perfectly regular smooth surface, while the upper limit 3 regards to the maximum allowed complexity of the irregular or rough surface [35].To date, many studies have revealed that surface fractality plays an important role in physicochemical processes such as diffusion, reaction kinetics, and adsorption [36],

Fractal Analysis
In recent decades, fractal analysis has been widely applied in a few fields of scientific researches to characterize the geometric and structural properties of fractal surfaces and pore structures [33,34].Fractal dimension is often adopted to quantitatively evaluate the irregularities of the fractal surface and pore structures.Its value varies from 2 to 3, in which the lowest value 2 corresponds to a perfectly regular smooth surface, while the upper limit 3 regards to the maximum allowed complexity of the irregular or rough surface [35].To date, many studies have revealed that surface fractality plays an important role in physicochemical processes such as diffusion, reaction kinetics, and adsorption [36], and the fractal concept can be adopted to elucidate the relationship between the adsorption performance and the surface structure of the sorbents.
One of the simplest and most popular relationships for determining the surface fractal dimension (D s ) of a solid by using adsorption isotherm data is the Frenkel-Halsey-Hill equation (FHH) [37,38], which in logarithmic form can be expressed as follows: where V is the nitrogen uptake at equilibrium pressure P, V m is the nitrogen uptake of a monolayer coverage, P 0 is the saturation pressure, A is a power-law exponent dependent on the surface fractal dimension and the adsorption mechanism, and C is a pre-exponential factor.Two limiting adsorption forces are considered: one is van der Waals at the early stages of adsorption, and the other is capillary condensation (surface tension) at later stages.At the early stage of adsorption, the van der Waals forces between gas-solid interactions are dominant and the gas-liquid surface tension forces are negligibly small.Then, the relationship between A and D s can be derived as follows However, for higher coverages at the later stage of adsorption, the interface is controlled by gas-liquid surface tension forces and the relationship between A and D s changes to the following expression The nitrogen uptake of the monolayer coverage can be obtained by using Brunauer-Emmett-Teller (BET) surface area calculation formula as follows 1 where P/P 0 is the relative pressure and c is a constant.Plot 1/[V(P/P 0 − 1)] versus P/P 0 , and linearly fits it in the P/P 0 range of 0.05-0.35 (Figures 9a  and 10a), the slope of the fitting curve is equal to (c − 1)/(cV m ), and the intercept of the fitting curve is equal to 1/cV m .Thus, the value of V m can be determined according to the slope and intercept of the fitting curve.Then, a plot of ln(V/V m ) versus ln(ln(P/P 0 )) fitting by using least-square method will show a linear trend (Figures 9b and 10b) as well, and the slope of the fitting line is equal to A, which can be used for calculating the value of the surface fractal dimension according to Equation (3).The surface fractal dimension of the fresh 5Fe5Ce/ZSM-5 is 2.61, and it considerably increases to 2.96 after the sulfidation reaction, which indicates a more sophisticated pore distribution for the spent 5Fe5Ce/ZSM-5, and the higher value suggests that the surfaces of the spent 5Fe5Ce/ZSM-5 is more irregular [39].

Conclusions
The Fe2O3/ZSM-5 composites modified with CeO2 are synthesized for H2S removal in the temperature range of 500-700 °C.The XRD and H2-TPR results show that the reducibility of Fe2O3/ZSM-5 is promoted by adding appropriate amounts of CeO2, and Fe2O3/ZSM-5 composites perform better by incorporating 30-50 at.% Ce 4+ ions into Fe2O3 lattices attributed to the cooperative effect of Fe2O3 and CeO2.The optimal sulfur capacity of 1020 µmol S/g over 5Fe5Ce/ZSM-5 is achieved at 600 °C, and the sulfidation process is in agreement with non-catalytic gas-solid redox reaction mechanism.The surface textural properties and the pore structures of the fresh and spent 5Fe5Ce/ZSM-5 sorbent is studied in the fractal theory point of view.The surface fractal dimension of 5Fe5Ce/ZSM-5 increases from 2.61 to 2.96 after sulfidation reaction probably attributed to the formation of numerous micropore structures of highly complexity and irregularity.

Conclusions
The Fe2O3/ZSM-5 composites modified with CeO2 are synthesized for H2S removal in the temperature range of 500-700 °C.The XRD and H2-TPR results show that the reducibility of Fe2O3/ZSM-5 is promoted by adding appropriate amounts of CeO2, and Fe2O3/ZSM-5 composites perform better by incorporating 30-50 at.% Ce 4+ ions into Fe2O3 lattices attributed to the cooperative effect of Fe2O3 and CeO2.The optimal sulfur capacity of 1020 µmol S/g over 5Fe5Ce/ZSM-5 is achieved at 600 °C, and the sulfidation process is in agreement with non-catalytic gas-solid redox reaction mechanism.The surface textural properties and the pore structures of the fresh and spent 5Fe5Ce/ZSM-5 sorbent is studied in the fractal theory point of view.The surface fractal dimension of 5Fe5Ce/ZSM-5 increases from 2.61 to 2.96 after sulfidation reaction probably attributed to the formation of numerous micropore structures of highly complexity and irregularity.

Conclusions
The Fe 2 O 3 /ZSM-5 composites modified with CeO 2 are synthesized for H 2 S removal in the temperature range of 500-700 • C. The XRD and H 2 -TPR results show that the reducibility of Fe 2 O 3 /ZSM-5 is promoted by adding appropriate amounts of CeO 2 , and Fe 2 O 3 /ZSM-5 composites perform better by incorporating 30-50 at.% Ce 4+ ions into Fe 2 O 3 lattices attributed to the cooperative effect of Fe 2 O 3 and CeO 2 .The optimal sulfur capacity of 1020 µmol S/g over 5Fe5Ce/ZSM-5 is achieved at 600 • C, and the sulfidation process is in agreement with non-catalytic gas-solid redox reaction mechanism.The surface textural properties and the pore structures of the fresh and spent 5Fe5Ce/ZSM-5 sorbent is studied in the fractal theory point of view.The surface fractal dimension of 5Fe5Ce/ZSM-5 increases from 2.61 to 2.96 after sulfidation reaction probably attributed to the formation of numerous micropore structures of highly complexity and irregularity.
2 and Fe 2 O 3 present fairly poor desulfurization performances with short breakthrough time of ~5 min and lower sulfur capacity of ~400 µmol S/g.The breakthrough time of Fe 2 O 3 -based sorbents is only 5-10 min by addition of 10-30 at.% CeO 2 , it suddenly increases to 20 min with CeO 2 molar fraction rising to 50 at.%.However, the breakthrough time and sulfur capacity slightly decrease to 15 min and 816 µmol S/g respectively with further addition of CeO 2 , possibly because some CeO 2 crystals dissolve out.The 5Fe5Ce/ZSM-5 (doping 50 at.% CeO 2 ) performs the longest breakthrough time of 20 min and the greatest sulfur capacity of 1020 µmol S/g, plausibly due to the intimate mixing of Fe 2 O 3 and CeO 2 .Colloids Interfaces 2017, 1, 10 5 of 11 further addition of CeO2, possibly because some CeO2 crystals dissolve out.The 5Fe5Ce/ZSM-5 (doping 50 at.% CeO2) performs the longest breakthrough time of 20 min and the greatest sulfur capacity of 1020 µmol S/g, plausibly due to the intimate mixing of Fe2O3 and CeO2.

Figure 9 .
Figure 9. Fractal analysis of fresh 5Fe5Ce/ZSM-5: (a) fitting curve for nitrogen uptake of a monolayer coverage and (b) fitting curve for surface fractal dimension.

Figure 10 .
Figure 10.Fractal analysis of spent 5Fe5Ce/ZSM-5: (a) fitting curve for nitrogen uptake of a monolayer coverage and (b) fitting curve for surface fractal dimension.

Figure 9 .of 11 Figure 9 .
Figure 9. Fractal analysis of fresh 5Fe5Ce/ZSM-5: (a) fitting curve for nitrogen uptake of a monolayer coverage and (b) fitting curve for surface fractal dimension.

Figure 10 .
Figure 10.Fractal analysis of spent 5Fe5Ce/ZSM-5: (a) fitting curve for nitrogen uptake of a monolayer coverage and (b) fitting curve for surface fractal dimension.

Figure 10 .
Figure 10.Fractal analysis of spent 5Fe5Ce/ZSM-5: (a) fitting curve for nitrogen uptake of a monolayer coverage and (b) fitting curve for surface fractal dimension.